CALCULUS Understanding Its Concepts and Methods

Vector arithmetic

The sum of the two vectors and is

Geometrically, the sum of two vectors is the diagonal of the parallelogram
whose sides are generated by the two
vectors.

The difference of the two vectors and is

This can be represented geometrically as the sum of the two vectors and .

The scalar multiple of a vector
by the scalar
*c*
is performed by multiplying each coordinate by the
scalar:

This has the effect of multiplying the length of the vector by
| *c* |,
maintaining the same direction if
*c*
is positive, and reversing direction if
*c*
is
negative.

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Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.